Dynamics of multisite phosphorylation. Multi-site phosphorylation dynamics is usually interpreted in terms of the processive and distributive mechanisms, which, in fact, are special limiting cases of the general phosphorylation dynamics. We study the phosphorylation dynamics in general, focusing on how these limiting cases arise for the special choice of the parameters Diffusion-limited trapping by patchy surfaces. In biological systems, diffusing solutes are typically trapped by active sites on the otherwise reflecting surfaces. We study trapping by patchy surfaces focusing on how the trapping rate depends on the patch surface fraction. Collective growth in simple cell networks. We study collective growth in a simple cell network with the goal to rationalize why different cells of the network grow with different rates. Non-trivial effects of the substrate dissociation rate on the enzymatic velocity. Based on general arguments, it was recently proposed that the enzymatic velocity can be increased by increasing the substrate dissociation rate. We study a general model of the multistate enzyme dynamics with the goal to specify the conditions under which such acceleration of the enzymatic reaction can occur. Bulk-mediated surface transport. We study surface transport of solute molecules which are allowed to dissociate from the surface and then come back. Our goal was to understand the origin of the anomalous subdiffusion of the molecules in such systems reported by different groups. Effect of stochastic gating on channel-facilitated membrane transport. Although stochastic gating in channel-facilitated membrane transport has been studied for many decades, there is no theory that explains how the solute flux through the channel depends on that gating rate and the solute dynamics in the channel. We developed such a theory which shows that significant deviations from the common sense expectation may occur at fast gating if the gating rate becomes comparable with the rate of the solute passage through the channel.